Question #efef9

1 Answer
Swarna Islam
Dec 20, 2017

#sqrt(1-sinx)=sin(x/2)-cos(x/2)#

Explanation:

#sqrt(1-sinx)=sqrt(sin^2(x/2)+cos^2(x/2)-2.sin(x/2)cos(x/2)##color(green)([As.sin^2theta+cos^2theta=1andsin2theta=2sinthetacostheta])#

#=sqrt((sin(x/2)-cos(x/2))^2##color(red)([As.a^2+b^2-2ab=(a-b)^2=(b-a)^2])#

#=sin(x/2)-cos(x/2)##color(brown)((Ans.))#

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